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MAE152Computer Graphics for Scientists and Engineers
Lighting in OpenGL
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Graphics: Conceptual Model
Real Object
Real Object
Human Eye
Human Eye
DisplayDevice
Graphics System
SyntheticModel
SyntheticCamera
Real Light
SyntheticLight Source
3
Lights, Surfaces, and Imaging
Proj. Plane
Viewer
Objects
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Lights, Surfaces, and Imaging
Proj. Plane
Viewer
Light Source
Objects
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Modes of Interaction of Light with Materials
SpecularSurface
DiffuseSurface Translucent
Surface
Note: Any given surface can have some of all three properties.
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Illuminating Surfaces
z
x
yI( ,,)
I(x, y, z,,, )We can define illumination function:To obtain total light, must integrate over total surface.
Itotal ( ) I(x, y, z, ,, ) dxdydz
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Simplified Model
Exact model can easily get complicated!Three simplifications help.
1. We can consider four classes of light sources
• ambient• point• spotlight• distant
2. Human color perception allows us to consider illuminationfunction in terms of the three primary colors.
3. We can neglect (OpenGL caveats):
• multiple reflections• obstruction of light path by objects
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Light SourcesAmbient light- no identifiable source or direction- hack for replacing true global illumination
= (light bouncing off from other objects)
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Ambient Light
Simulates situations where light sources are designed to produceuniform lighting throughout a scene.
Characterized by a scalar intensity, Ia , that is identical at every pointin the scene.
Ia Iar
Iag
Iab
Although every surface receives the same illumination, eachsurface can reflect the light differently.
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Point Sources
An ideal point source radiates equally in all directions. It canbe characterized by:
I(p0 ) I r (p0 )
Ig (p0 )
Ib (p0 )
Intensity of illumination from a point source is proportionalto the inverse square of the distance between the point and theilluminated surface.
I(p,p0 ) 1
p p0
2 I(p0 )
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Light Sources
Types of light sources
- glLightfv(GL_LIGHT0,GL_POSITION,light[])
- directional/parallel lights= real-life example: sun= infinitely far source: homogeneous co-ord. w=0
- point lights= same intensity in all directions
- spot lights= limited set of directions:
point+direction+cutoff angle
0
z
y
x
1
z
y
x
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Spotlights
Spotlights are point sources for which the angle through whichlight has been emitted has been limited.
l
s
I k cose ( ) k(ls)e
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Distant Sources
Most shading calculations require the direction from the point ona surface to the light source. As light sources are moved to larger distances, this direction approaches a constant.
Therefore the point source location will be replaced by a vectorindicating the direction of the source.
p0
x
y
z
1
will be replaced by : p0
x
y
z
0
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Lighted Sphere Demo and Source Code
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Reflection
Rough Surface:Light is reflected equally in all directions.
Diffuse
Smooth Surface:Light is reflected at an anglenear to the incident angle.Specular
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Vectors Used byPhong Lighting Model
p is an arbitrary point on a surface.n is the unit normal to the surface at p.l is a unit vector in the direction of the light source.r is a unit vector in the direction of a perfectly (specular) reflectionv is a unit vector in the direction of the viewer.
n
l r
v
p
Viewer
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Elements of the Phong Lighting Model
R i Rira Riga Riba
Rird Rigd Ribd
Rirs Rigs Ribs
At each point p there is a reflection matrix forthe ith light source:
I Ia Id Is La Ra Ld Rd Ls Rs
Assuming the calculations will be done separately foreach primary, we can sum over light sources to get:
L i Lira Liga Liba
Lird Ligd Libd
Lirs Ligs Libs
At each point p thereis an illumination matrixfrom the ith light source:
red green blue
ambient
diffuse
specular
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Elements of the Phong Lighting ModelAmbient Reflection
Ia ka La
0 ka 1
The intensity of ambient light is the same at every pointon the surface. The percentage of light reflected is givenby: Ra ka
Note that the ambient reflection terms can be differentfor red, green and blue.
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Elements of the Phong Lighting ModelDiffuse Reflection
Intensity of illumination is dependent upon the incidence angleof light from the source:
Adding a term for attenuationwith distance from source:
Id kd
a bd cd 2(ln)Ld
l
n
Rd cos ln
Id kd (ln)Ld
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Elements of the Phong Lighting ModelSpecular Reflection
For a shiny surface, most light is reflected around vector r,corresponding to a reflected angle equal to the angle of incidence.If is the angle between v and r,
Is ks Ls cos Adding a distance term, and expressing the cosine in terms ofa dot product:
Is 1
a bd cd 2ks Ls (r v)
n
l r
v
p
Viewer
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The Complete Lighting Model
globalambglobalambm
aassdd
n
i
LkE
LkLkLkcdbda
I
)])()((1
[2
1
0
vrnl
Distance(Attenuation)
Ambient
Diffuse Specular
EmissionGlobalAmbient
n
l r
v
p
Viewer
()
()
()
glMaterial
glLight
elglLightMod
k
L
E
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Calculation of Normals
Normal exists at every point for mathematically defined smooth surfaces.
Exists for each polygon in surface defined by flat polygons.What about the shared lines/points?
Polygonal Case:
p0
p1
p2
n
n (p1 p0 ) (p2 p0 )
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Calculation of NormalsMathematically Defined Surface: Sphere
Sphere is defined implicitly by equation:
f (x, y, z) x2 y2 z2 1 0
n
f
xf
yf
z
2x
2y
2z
2p
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Specification of the Normal in OpenGL
Specification of the current normal is modal and associated withvertices.
glNormal3f(nx,ny,nz);glNormal3fv(pointer_to_normal_vector);
You have to calculate the normals yourself.
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Shading in OpenGL:Flat Shading
OpenGL uses the normal of the first vertex of a single polygon to determine the color.
Requested by: glShadeModel(GL_FLAT);
Flat shading exaggerates the visual effect of the boundaries between polygons due to the Mach band effect.
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Mach Band Effect(Mach, 1865)
Color Science, Concepts and MethodsWyszecki, Stiles
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Mach Band Effect
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Mach Band Effect
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Shading in OpenGL:Smooth Shading
Requested by: glShadeModel(GL_SMOOTH);
Lighting calculations will be done at each vertex using the material properties, and the vectors v and l calculated for that vertex.
Bilinear interpolation is used to determine color values in the interior of the polygon.
Gouraud Shading:
Normal at a vertex is the normalized average of the normals of the polygons that share that vertex.
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Gouraud Shading
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Lighting Implementation in OpenGL
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Lighted Sphere Demo and Source Code
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Enable Depth BufferFor Hidden Surface Removal
//before enablingwhile (1) { get_viewing_point_from_mouse_position(); glClear(GL_COLOR_BUFFER_BIT); draw_3d_object_A(); draw_3d_object_B(); }
//after enablingglutInitDisplayMode (GLUT_DEPTH | .... ); glEnable(GL_DEPTH_TEST); ... while (1) { glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); get_viewing_point_from_mouse_position(); draw_3d_object_A();draw_3d_object_B();}
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Specifying Light Sources in OpenGL
General form: glLightf(source, parameter, value); glLightfv(source, parameter, *array);
source is one of at least eight lights: GL_LIGHTi
Parameters:
GL_AMBIENT contains four values that specify the ambient RGBAintensity of the light. Default is (0.0, 0.0, 0.0, 1.0).
GL_DIFFUSE contains four values that specify the diffuse RGBAintensity of the light. Default is (1.0, 1.0, 1.0, 1.0).
GL_SPECULAR contains four values that specify the secular RGBAintensity of the light. Default is (1.0, 1.0, 1.0, 1.0).
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Specifying Light Sources in OpenGLGeneral form: glLightf(source, parameter, value); glLightfv(source, parameter, *array);
GL_POSITION specifies the position of the light in homogeneousobject coordinates. If the w component is zero, the lightis treated as a directional source.
GL_SPOT_DIRECTION specifies the direction of the light in homogeneous object coordinates. Default is (0.0, 0.0, -1.0)
GL_SPOT_EXPONENT spotlight exponent, default 0.0
GL_SPOT_CUTOFF spot cutoff angle in [0,90] or (default) 180.
l
s
I k cose ( ) k(ls)e
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Specifying Light Sources in OpenGLGeneral form: glLightf(source, parameter, value); glLightfv(source, parameter, *array);
GL_CONSTANT_ATTENUATION constant atten. factor, default 1.0
GL_LINEAR_ATTENUATION linear atten. factor, default 0.0
GL_QUADRATIC_ATTENUATION quadratic atten. factor, default 0.0
Id kd
a bd cd 2(ln)Ld
n
l rv
p
Viewer
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Enabling the Lights and Lighting
Enabling a specific light source: glEnable(GL_LIGHTi );
Enabling the lighting model: glEnable (GL_LIGHTING);
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Specifying Materials in OpenGL
General form: glMaterialf(face, parameter,value); glMaterialfv(face, parameter,*array);
face is GL_FRONT, GL_BACK, GL_FRONT_AND_BACK
parameter is:
GL_AMBIENT four values that specify the ambient RGBA reflectance of the material. (0.2,0.2,0.2,1.0)
GL_DIFFUSE four values that specify the diffuse RGBA reflectance of the material. (0.8,0.8,0.8,1.0)
GL_SPECULAR four values that specify the ambient RGBA reflectance of the material. (0.0,0.0,0.0,1.0)
GL_SHININESS specifies the specular reflectance exponent of the material. 0.0
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1. Ambient light in a scene with 3
spheres.
2. Diffuse light hitting the surface
of 3 spheres. Notice, the spheres
look matte and almost plastic like.
3. The three spheres illuminated by specular light. Imagine an extremely shiny billiard ball and the sheen it creates
Types of Light and effects
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Demo
Rotating light
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End of Lighting